I have known of shooters sticking the barrels into a drum of water for a few seconds in a high volume shooting situation to cool them. I think it was at a flurry shoot. Pull them out and the remaining heat evaporates any moisture in a few seconds.
Re: the .410, I recently shot a .410 S x S sporting clays course and was reminded how uncomfortable they get, and how quickly. After each station I had to try and cool them down before the next. Perhaps it is only perception, and because the fingers wrap around the little splinter forend and barrels so much more readily it becomes more apparent. I dunno. I do know the more people shooting on your squad, the cooler your barrels will be when you get to the next station.

SRH